A comparative study on crash-inﬂuencing factors by facility ......A comparative study on...

A comparative study on crash-influencing factors by facility typeson urban expressway

Yong Wu • Hideki Nakamura • Miho Asano

Received: 1 July 2013 / Revised: 15 October 2013 / Accepted: 18 October 2013 / Published online: 30 November 2013

� The Author(s) 2013. This article is published with open access at Springerlink.com

Abstract This study aims at identifying crash-influencing

factors by facility type of Nagoya Urban Expressway,

considering the interaction of geometry, traffic flow, and

ambient conditions. Crash rate (CR) model is firstly

developed separately at four facility types: basic, merge,

and diverge segments and sharp curve. Traffic flows are

thereby categorized, and based on the traffic categories, the

significances of factors affecting crashes are analyzed by

principal component analysis. The results reveal that, the

CR at merge segment is significantly higher than those at

basic and diverge segments in uncongested flow, while the

value is not significantly different at the three facility types

in congested flow. In both un- and congested flows, sharp

curve has the worst safety performance in view of its

highest CR. Regarding influencing factors, geometric

design and traffic flow are most significant in un- and

congested flows, respectively. As mainline flow increases,

the effect of merging ratio affecting crash is on the rise at

basic and merge segments as opposed to the decreasing

significance of diverging ratio at diverge segment. Mean-

while, longer acceleration and deceleration lanes are

adverse to safety in uncongested flow, while shorter

acceleration and deceleration lanes are adverse in con-

gested flow. Due to its special geometric design, crashes at

sharp curve are highly associated with the large centrifugal

force and heavy restricted visibility.

Keywords Crash-influencing factors � Crash rates �Principal component analysis � Facility types � Urban

expressway

1 Introduction

Improving traffic safety is a worldwide issue to be relieved

urgently. Crash characteristics and their influencing fac-

tors, as the theoretical basis for safety improvement, may

provide direction for policies and countermeasures aimed

at smoothing hazardous conditions. For a better under-

standing of crash-influencing factors, researchers have

continually sought ways through an extensive array of

approaches, and the most prominent one is crash data

analysis [1]. The conventional approaches have established

statistical links between crash rate (CR) and its explanatory

factors [2, 3]. In the analyses, traffic flows are generally

represented by low-resolution data that is collected at a

highly aggregated level, e.g., hourly or daily flows. Geo-

metric features are primarily considered the hierarchy of

radius or slope [4, 5]. Meanwhile, several studies have

suggested that crashes are associated with the interaction of

geometry, traffic flow, and ambient conditions [6]. How-

ever, most existing studies investigated the factors indi-

vidually and the related CR models were developed based

on single factor only. As a result, it is inadequate to identify

the nature of individuals through aggregated analysis only,

since the conditions preceding individual crashes are vir-

tually different from each other [1].

Considering the insufficiency of CR analysis above,

some studies have tried to identify crash characteristics at

individual level, in an effort to predict crash risk on a real

time basis [7–9]. Through these studies, the effect of traffic

flow on crash risk has been well analyzed. In theory, the

concept of real-time crash prediction exhibits huge promise

for the application of proactive traffic management strate-

gies for safety.

However, the combined effects of geometry, traffic flow,

and ambient conditions on crashes still have not been well

Y. Wu (&) � H. Nakamura � M. Asano

Department of Civil Engineering, Nagoya University,

C1-2(651) Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan

e-mail: [email protected]

123

J. Mod. Transport. (2013) 21(4):224–235

DOI 10.1007/s40534-013-0024-9

anayzed through the above studies. Furthermore, these

papers primarily developed crash model for the whole

traffic conditions, which may conflict with the fact that the

influence of traffic flow on crashes may vary when traffic

conditions change. In addition, even if crash characteristics

are found out to be dependent on facility type that is

composed of uniform segment individually, e.g., basic,

merge, and diverge segments [2], the existing studies are

focused on the entire route of intercity expressway without

segmentation.

Another cause for the limited predictive performance of

existing models is the inadequacy of analytic process [10].

As for statistical methods, the significance and indepen-

dence of explanatory variables should be identified in

advance for the reliability of statistics. Whereas, many

previous studies paid little attention to this point and

incorporated the potential influencing factors into crash

modeling directly.

Urban expressway is one common type of separated

highway with full control of access in large cities in Japan.

Generally, it is composed of various facility types where

geometric features and traffic characteristics are often

different from each other. Correspondingly, crash charac-

teristics and their influencing factors may also be different

by facility type. In the meantime, compared to intercity

expressway, crash characteristics and their related influ-

encing factors of urban expressway are different [11].

Necessarily, urban expressway deserves to be analyzed

independently and its crash characteristics should be

identified based on specific facility type.

Given the problems of existing studies, the objective of

this paper is to investigate crash characteristics based on

CR models and their influencing factors by facility type on

urban expressway. Meanwhile, the causes are identified by

considering the interaction of geometry, traffic flow, and

ambient conditions. Besides, geometric features are iden-

tified considering the driver-vehicle-roadway interaction.

The significances of these factors affecting crashes are

compared at different facility types using principal com-

ponent analysis (PCA). Their influencing mechanisms are

further discussed. In essence, this study can be regarded as

a proactive analysis for crash risk prediction model in the

future.

2 Study sites and datasets

2.1 Study sites

The test bed of this study is Nagoya Urban Expressway

network (NEX) as shown in Fig. 1. Up to December 31,

2009, this network was about 69.2 km 9 2 (two direc-

tions) in total length with over 250 ultrasonic detectors

installed with an average spacing of 500 m (varied in

250–750 m) on mainline. Most routes are 4-lane road-

ways (2-lane/dir), except the inner ring (Route no. R) that

is one-way roadway and where the number of lanes dif-

fers (2–5) with the change of ramp junctions. In the

limited areas, such as the links of other routes to the inner

ring, small curves are designed. In this network, two

recurrent bottlenecks are located along Odaka line (Route

no. 3).

Five databases are used in this study; (1) crash records

with the occurrence time in minutes, the location in 0.1 km

and the weather and pavement conditions; (2) detector data

including traffic volume q, average speed v, and occupancy

occ per 5 min; (3) geometric design and the location of

detector in 0.01 km; (4) traffic regulation records for

incidents (e.g., crash, working, and inclement weather)

including the locations and periods of temporal lane and

cross-section closures; and, (5) daily sunrise and sunset

time records in Nagoya. Here, it is worth noting that

detector data are processed for the whole cross section of

each direction. The period of the data above is for 3 years

(2007–2009) except for those on Kiyosu line (Route no. 6)

that was opened from December 1, 2007.

Fig. 1 Schematic map of NEX network (2009) (Source Nagoya

Expressway Public Corp., modified by authors)

Comparative study on crash-influencing factors 225

123J. Mod. Transport. (2013) 21(4):224–235

2.2 Segmentation of facility types

Basic segment is extracted outside the 500 m up- and

down-stream of ramp junctions considering the experience

in Japan [12]. Correspondingly, merge or diverge segments

are regarded as the sections inside the 500 m up- and

down-stream of on- and off-ramps, respectively. The seg-

mentation methods are shown in Fig. 2. Other than these

segments, there is a special geometric design in NEX,

curve with small radius. Figure 3 explains CR statistics

dependent on radius. Obviously, compared to other seg-

ments, much higher CR exists in the curves with radius

smaller than 100 m. Thus, these curves are defined as sharp

curves and regarded as another distinct facility type of

NEX. Given the limitation of segment samples available,

basic, merge, and diverge segments, and sharp curve will

be analyzed in this study.

The cross sections of inner ring are diverse and the

length of individual layouts, i.e., 2-, 3-, 4-, or 5-lane, is not

enough to be separately analyzed. Meanwhile, all of the

sharp curves along Inner ring are 2-lane roadway. In this

regard, only 2-lane segments are analyzed in this study and

the geometric statistics by facility types are summarized in

Table 1.

3 Methodology

3.1 Data extraction

3.1.1 Detector data

In principle, detectors can count the number of vehicles at

their locations only. In such case, the ‘‘coverage area’’ of

detector is defined for estimating traffic conditions at crash

locations through detector data. At basic segment, the

boundary of two consecutive coverage areas is defined at

the midpoint between two neighboring detectors. At merge

and diverge segments, it is bounded at the ramp-junction

point, and one segment can be divided into up- and down-

stream areas. Each sharp curve can be matched with a

single detector. Note that the time of crash is recorded by

road administrators after the crash occurrence. In reality, it

does not correspond to occurrence time exactly. For this

reason, data within small time before crashes should be

rejected to avoid mixing up crash-influencing and crash-

influenced data. Therefore, the latest data at least 5 min

before the recorded time are accepted after the exclusion of

invalid data and the data within lane and section-closure

intervals in advance.

3.1.2 Geometric features

Design consistency is the conformance of geometry of a

highway with driver expectancy, and its importance and

significant contribution to road safety is justified by

understanding the driver–vehicle–roadway interaction [13]

that may vary at individual locations in nature. In this

regard, geometric variation in the upstream of crash loca-

tion is proposed to reflect the effect of geometry on cra-

shes. Considering the length of detector coverage area, the

following variables in 500 m distance are extracted [12].

Basic segment

Basic segment

Merge segment

Diverge segment

Tight curve

0.5 km 0.5 km

0.5 km

0.5 km

0.5 km

0.5 km

R<100 m

Fig. 2 Segmentation of facility types

0

5

10

15

20

25

10 100 1000 10000 100000

Cra

sh ra

te (

cras

h/10

6 VK

MT

)

Radius (m)

Much higher CR

Fig. 3 Distribution of crash rate to radius

Table 1 Geometric statistics of facility types

Facility type No. of segments Total length (km)

Basic segment 38 56.6

Merge segment 28 20.9

Diverge segment 35 25.2

Sharp curve 9 2.5

226 Y. Wu et al.

123 J. Mod. Transport. (2013) 21(4):224–235

(1) Variation in road elevation h between the crash

location and its 500 m upstream, and the maximum ele-

vation difference H in this 500 m distance (Fig. 4).

(2) Horizontal displacement S. Radius is impossible to

describe a section composed of various curves. On the

other hand, centrifugal force is also associated with the

horizontal displacement s in the direction of tangent to the

curve j (Fig. 5). In such case, S in the 500 m distance (Rsj)

is adopted and calculated by the following equations.

hj ¼Lj

Rj

ð0 [ ; hj � p=2Þ; ð1Þ

sj ¼ Rjð1 � cos hjÞ; ð2Þ

where j is the ID of curve. Rj, hj, Lj, and sj correspond to the

radius, central angle, arc length, and horizontal displace-

ment of curve j, respectively.

(3) Index of centrifugal force ICF. Speed v always has a

square relation with centrifugal force. This study designs

ICF (ICF = Sv2) to reflect the combined effect of speed

v and horizontal displacement S, while it is not centrifugal

force.

(4) Index of space displacement ISD. ISD (ISD = SH) is

used to reveal the comprehensive geometric features

induced by horizontal and vertical variation in this study.

The geometric data above are collected every 0.1 km as

crash is recorded in a unit of 0.1 km. Besides, these data

are also extracted at the location of detector that is the

common link between crash and detector data. Table 2

summarizes the process of data collection.

3.1.3 Ambient conditions

Common, prevailing, and uncontrolled environment and

weather conditions are defined as ambient conditions. They

are (1) ambient light classified into daytime and nighttime,

which are the period from sunrise to sunset and from sunset

to sunrise, respectively; (2) sunny, cloudy, and rainy

weather conditions at the time of crash; (3) dry and wet

pavement conditions at the location of crash; and, (4) day

type on crash days including holiday and weekday. Here,

holiday includes all weekends, and all national and tradi-

tional holidays like the Golden Week in May and the Obon

Week in August in Japan.

3.1.4 Data matching

The related detector data, geometric features, and ambient

conditions for individual crashes are matched as exempli-

fied in Table 3. The crashes matching with invalid detector

data and within lane and cross-section closure intervals are

excluded in advance. As a result, a total of 1,591 crashes

remain for the following analysis.

h(>0) H

h(>0) H

500m upstream

Crash location

Crash location

500m upstream

Fig. 4 Variation in road elevation

sj

S

Lj

Lj+1

Sj+1

Rj

Rj

Rj+

1

θj

θ j+1

Fig. 5 Horizontal displacement

Table 2 Example of geometric variations collection

Route

no.

Direction* Kilopost** h (m) H (m) S (m) ISD

(m2)

1 SB 0.0 -4.63 5.49 0.78 4.30

1 SB 0.1 -7.90 8.49 3.91 33.2

1 SB 0.2 -10.6 11.5 6.08 69.9

1 SB 0.21 -11.5 11.8 8.88 104.7

1 SB 0.3 -15.3 15.3 9.60 146.9

1 SB – – – – –

1 SB 6.4 10.2 10.9 5.15 56.1

*SB South-bound

** 0.21: the Kilopost of detector #0101


123J. Mod. Transport. (2013) 21(4):224–235

3.2 Classification of traffic conditions

Congested flow, characterized by traffic oscillation, has

different features from uncongested flow. It is necessary to

make a distinction between two traffic regimes. Figure 6

shows the traffic volume–speed diagram at Horita on-ramp

junction, one typical bottleneck in NEX. The speed of

60 km/h, corresponding to maximal flow is defined as the

critical speed vc that is used for classifying un- and con-

gested flows [2, 14]. Besides, the corresponding value at

another bottleneck (Takatsuji on-ramp junction) is also

found out around 60 km/h.

The value of 60 km/h would be regarded as the related

index at basic and diverge segments, since no bottleneck can

be virtually found at both segments in NEX. At sharp curve, a

threshold speed of 45 km/h is selected in general for clas-

sifying two traffic regimes based on traffic flow-speed dia-

gram at Tsurumai curve (Fig. 7). The value is further

checked at other sharp curves, and it is found out to be reli-

able for classifying un- and congested flows basically.

To reflect the variation in traffic characteristics, each

traffic regime is further sub-classified. It is evident that

speed has a high variance at low flow rates (see Figs. 6 and

7). Besides, occupancy is not a commonly used index.

Thus, traffic density k calculated by Eq. (3) is proposed to

be the measure of effectiveness to further classify the

traffic conditions. In view of the number of crash samples

available, the aggregation intervals of k are set as 10 and

30 veh/km for un- and congested flows, respectively.

kei ¼12 � qi

vi

; ð3Þ

where qi and vi denote traffic flow and average speed in

5 min # i, respectively. kei corresponds to the calculated

traffic density in this 5 min.

3.3 Calculation of crash rate (CR)

CR for traffic condition n can be calculated by the fol-

lowing equation:

CRn ¼ NOCn � 106

PQnlLl

; ð4Þ

where n and l are the ID of traffic condition and coverage

area, respectively; NOCn is the number of crashes for

traffic condition n. QnlLl is the value of vehicle kilometers

traveled (VKMT) in detector coverage area l for traffic

condition n.

Table 3 Examples of data matching for individual crashes

Crash

ID

Traffic characteristics Geometric features Ambient conditions

q (veh/

5 min)

v (km/h) MR DR Facility

typeah (m) H (m) ICF

(km3/h2)

ISD

(m2)

LAb

(m)

LDb

(m)

Light Weather Pavement Day type

1 139 88.7 – – B 1.5 1.5 0 0 – – Day Sunny Dry Holiday

2 96 95.0 – 0.02 D 0.5 1.3 302 45 – 220 Day Sunny Dry Weekday

3 29 80.3 – – S 10.3 12.7 126 249 – – Night Cloudy Wet Holiday

4 154 82.9 0.07 – M 1.5 1.5 0 0 200 – Day Cloudy Dry Weekday

B, M, D, and S basic, merge, and diverge segments, and sharp curve, respectively, LA length of acceleration lane at merge segment, LD length of

deceleration lane at diverge segment

0 10 20 30 40 50 60 70 80 90

100 110 120

0 25 50 75 100 125 150 175 200 225 250 275 300 325 350

Ave

rage

spe

ed (k

m/h

)

Traffic volume (veh/5-min)

Critical speed: 60km/h

High speed variability at low flow rates

Max. flow

Uncongested flow

Congested flow

Fig. 6 q–v diagram at Horita on-ramp junction

0

10

20

30

40

50

60

70

80

90

0 25 50 75 100 125 150 175 200 225 250 275 300

Ave

rage

spe

ed (k

m/h

)

Traffic volume (veh/5-min)

Threshold speed: 45km/h

Uncongested flow

Congested flow

High speed variability at low flow rates

Fig. 7 q–v diagram in Tsurumai curve

228 Y. Wu et al.

123 J. Mod. Transport. (2013) 21(4):224–235

3.4 Principal component analysis (PCA)

PCA is a powerful tool for reducing a large number of

observed variables into a small number of artificial vari-

ables that account for most of the variance in the dataset

[15]. In general, through orthogonal transformation, a set of

observations of possibly correlated variables can be con-

verted into a set of values of linearly uncorrelated vari-

ables. Those converted values are defined as principal

components. Technically, a principal component can be

regarded to be a linear combination of optimally weighted

observed variables [15]. As a result, the components are

ranked in the order of accounting amount of total variance

in the observed variables. Then, two criteria are generally

available to select the number of component extracted: (1)

80 % rule, the extracted components should be capable to

explain at least 80 % of the variance in the original dataset.

(2) Eigen value rule, only components whose eigen values

are over 1.0 can be retained.

4 Crash rate estimation models

In the following, the differences of crash characteristics by

facility type are investigated by comparing CR models

based on traffic conditions.

4.1 Uncongested flow

Figure 8 gives the CR tendency following traffic density

k by facility type in uncongested flow. It is evident that

sharp curve has a special characteristic compared to other

segments. Its CR is the highest among four facility types at

low-density stages. Then, the value follows a decreasing

tendency to k. In contrast, the CR at other segments

increases as k increases. Such phenomenon may be related

to the design of small radius for sharp curve. Such geo-

metric design can result in high centrifugal force that can

act on the vehicle and tries to push it to the outside of the

curve. Furthermore, higher speed may result in higher

centrifugal force.

Regarding the differences at other segments, CR at

merge segment increases rapidly at high-density stages and

gets much higher compared to basic and diverge segments.

The results of paired t-test at the three facility types in

Table 4 also reveal that CR at basic/diverge segments is

significantly lower than that at merge segment, while they

are not significantly different from each other between

basic and diverge segments. At merge segment, merging

maneuvers can result in slow-down and lane-changing

behaviors for mainline traffic. These interruptions may

increase the possibility of vehicle conflicts. Such possi-

bility can further increase with an increase in k.

Table 5 summarizes the CR regression models as

function of k as well as the goodness-of-fit of models at

four facility types. At sharp curve, the model is power

function while they are quadratic functions at other facility

types. All of the models and variables are significant at

95 % confidence level (not shown in Table 5). Regarding

quadratic models, CR at merge segment is most sensitive to

the increase in k, more than three times of CR increases as

that at basic and diverge segments by the increase in one

unit of k.

4.2 Congested flow

Figure 9 describes the differences of CR distribution to

k by facility type in congested flow. It appears that CR

follows increasing tendencies to k at four facility types. In

contrast to other segments, sharp curve still has the highest

CR in congested flow while no statistical regression model

is developed at this facility type due to the limited crash

samples. Since the differences of CR tendency at other

segments are not clear in Fig. 9, a paired t-test is conducted

as shown in Table 6. The results indicate that there is no

112

97

36 32 31

11

55

72

21 28

48

28

81 73

22 14

8 6

228

123

64

42 30 26

0

5

10

15

20

25

30

0

50

100

150

200

250

300

5 15 25 35 45 55

Cra

sh ra

te (c

rash

/106 V

KM

T)

Num

ber o

f cr

ashe

s

Traffic density (veh/km)

NOC at basic segmentNOC at merge segmentNOC at diverge segmentNOC at sharp curveCR at basic segmentCR at merge segmentCR at diverge segmentCR at sharp curve

Fig. 8 CR comparison in uncongested flow

Table 4 T-test of CR in uncongested flow

Paired t-Value df Sig.

Pair 1: basic and merge segments -2.781 5 0.019

Pair 2: basic and diverge segments -1.070 5 0.310

Pair 3: merge and diverge segments 2.320 5 0.043


123J. Mod. Transport. (2013) 21(4):224–235

significant difference of CR at basic, merge, and diverge

segments. Such finding may imply that the effect of facility

type on crashes is reduced in congested flow. For this

reason, CR model is developed by combining the three

facility types in order to increase the number of crash

samples for reliability. As demonstrated in Table 7, an

exponential function is adopted and it fits well to the

combined CR tendency. The model and its variables are

also significant at 95 % confidence level, while the results

are not shown in Table 7.

5 Effects of influencing factors

The analyses above reveal that CR characteristics are

different by facility type, which may be related to the

different geometric designs and traffic characteristics.

However, CR analysis is insufficient to examine a variety

of factors by a single model. Instead, PCA is applied and

the affecting mechanisms of individual factors are further

investigated.

5.1 Introduction of variables

Table 8 explains individual variables combining with its

type and some summary statistics. In nature, traffic flow

diagram is two-dimensional, and k and v are used together

to describe traffic conditions. As for geometric features, h,

ICF, and ISD are picked out to reflect the vertical, hori-

zontal, and comprehensive geometric variations, respec-

tively. Dummy variables are referred to incorporate

ambient conditions into PCA. A dummy variable usually

takes 0 and 1. In this case, weather conditions (over 2

categories) are replaced by pavement conditions (only 2

categories), since two conditions are usually highly related

to each other.

At merge and diverge segments, ramp traffic is a sig-

nificant influencing factor on crashes [16]. This study

employs ramp flow ratio to illustrate the interaction

between ramp and mainline traffic. Merging ratio (MR) or

diverging ratio (DR) is defined as the proportion of on- or

off-ramp traffic out of the sum of ramp and mainline traffic,

respectively. Meanwhile, the length of acceleration lane LA

or the length of deceleration lane LD is adopted to reveal

the space available provided for merging or diverging

maneuvers, respectively.

Table 5 CR regression models in uncongested flow

Facility type Sample size Modela

B 319 crashes CR = 6.81 9 10-4k2-3.23 9 10-2k ? 0.541, R2 = 0.998, k(CRmin) = 24

M 25 l crashes CR = 2.55 9 10-3k2-9.29 9 10-2k ? 1.01, R2 = 0.983, k(CRmin) = 20

D 204 crashes CR = 5.68 9 10-4k2-3.34 9 10-2k ? 0.747 R2 = 0.849 k(CRmin) = 28

S 513 crashes CR = 132.2k-0.983, R2 = 0.992

a k (CRminimal): traffic density corresponding to the minimal CR

33

45

29

20

11

31

43

12

5

23

14

7 4

16

6 5

0

5

10

15

20

25

30

35

40

45

0

10

20

30

40

50

60

70

80

90

55 85 115 145 175

Cra

sh ra

te (

cras

h/10

6V

KM

T)

Num

ber o

f cr

ashe

s

Traffic density (veh/km)

NOC at basic segmentNOC at merge segmentNOC at diverge segmentNOC at sharp curveCR at basic segmentCR at merge segmentCR at diverge segmentCR at sharp curve

Fig. 9 CR comparison in congested flow

Table 6 T-test of CR in congested flow

Paired t-Value df Sig.

Pair 1: basic and merge segments -2.448 4 0.092

Pair 2: basic and diverge segments -0.153 4 0.888

Pair 3: merge and diverge segments 0.325 4 0.767

Table 7 CR regression model in congested flow

Facility type Sample size Model

B ? M ? D 513 crashes CR = 4.87 9 10-1e0.0155k R2 = 0.924

230 Y. Wu et al.

123 J. Mod. Transport. (2013) 21(4):224–235

5.2 PCA among various facility types

In essence, PCA rotates data by using a linear transfor-

mation. Consequently, only the monotonic loadings of

factors can be reflected by this approach. For this reason,

uncongested flow is further classified into low-and high-

density conditions at approximately 25 veh/km in view of

the value of k (CRmin) as shown in Fig. 10, since there are

different monotonicities of CR model in two conditions. As

a result, three traffic conditions are analyzed, i.e., low- and

high-density uncongested flow as well as congested flow.

5.2.1 Low-density uncongested flow

Table 9 demonstrates PCA results at basic segment in low-

density uncongested flow. In terms of the rules introduced

in Sect. 3.4, four components are selected and all of the

factors can explain at least 80 % of variance in the original

dataset in terms of the value of cumulative percent.

In low-density uncongested flow, crashes at basic seg-

ment are found to be significantly associated with geo-

metric variation (ICF and ISD), traffic density along with

ambient light, speed coupled with pavement, and vertical

variation h. Geometric variation is the 1st component, as

great variation may result in frequent speed reduction.

Accordingly, the difficulty for drivers to control vehicle

behaviors increases. At low traffic density k, driver’s

attention is not high, and some discretionary behaviors may

be operated. Such condition combining with the poor

ambient light is possible to increase crash risk. Meanwhile,

due to the reduced value of tire-pavement friction, high

speed v combining with wet pavement can reduce the

roadability. In such cases, k and v are two separate com-

ponents, which can further demonstrate that both variables

are not highly interrelated at low flow rate. In addition,

vertical variation h has a positive loading because of the

increased visibility restriction and the difficulty in main-

taining vehicle behaviors for drivers.

Principal components at other segments are analyzed as

shown in Table 10. The variables that are significantly

related to each component are selected based on their

loadings. For judging the relative significance of the same

component by facility type, the percent of variance

explained by each component is provided as well.

One difference at merge segment from basic segment is

that MR combining with the length of acceleration lane LA

becomes a principal component. Meanwhile, day type is

found to be significant. In terms of the percent of variance

accounted by components, the significance of geometric

variation gets lower in contrast to basic segment. Merging

traffic is an important influencing factor, since it can induce

interruption to mainline traffic. Such interruption may get

stronger as MR increases. Besides, higher LA can provide

more space for ramp and mainline traffic to adjust for

Table 8 Introduction of individual variables

Variables Statisticsa Description

Max. Min.

k 238 0 Traffic density (veh/km)

v 141.0 4.7 Average speed (km/h)

MR 0.78 0.00 Merging ratio

DR 0.60 0.00 Diverging ratio

ICF 1997 0.1 Index of centrifugal force (km3/h2)

h 14.8 0.1 Vertical variation (m)

ISD 1112.7 0.0 Index of space displacement (m2)

LA 250 100 Length of acceleration lane (m)

LD 432 100 Length of deceleration lane (m)

Pave f(1) = 27.7 % Equal to 1 if wet pavement, 0 otherwise

Light f(1) = 27.1 % Equal to 1 if nighttime, 0 otherwise

Day f(1) = 29.4 % Equal to 1 if holiday, 0 otherwise

f frequencya Max./Min.: maximal and minimal values, respectively

Congested flow

Uncongested flow

Low-density High-density

vc

0Traffic volume (q)

Spee

d (v

)

ke=2

5 ve

h/km

vC=60 km/h (basic/merge/diverge segments)vC=45 km/h (tight curve)

Fig. 10 Classification of traffic conditions

Table 9 PCA results at basic segments

Variables Component

1st 2nd 3rd 4th

ke -0.194 -0.852 -0.119 0.103

v 0.285 0.182 0.798 -0.086

ICF 0.953 0.005 0.053 -0.122

ISD 0.959 0.011 -0.044 0.090

h 0.119 0.149 0.228 0.973

Pave 0.294 0.214 0.783 -0.095

Day 0.139 0.093 0.190 -0.468

Light -0.164 0.838 -0.130 0.143

Initial Eigenvalue 2.12 1.54 1.37 1.12

Percent of variance 30.3 20.2 18.2 15.1

Cumulative Percent 30.3 50.5 68.7 83.8

The variables highly related to each component are in bold


123J. Mod. Transport. (2013) 21(4):224–235

merging behaviors. Regarding the influence of day type on

crashes, it may be related to the different vehicle compo-

sitions and driver populations between holiday and week-

day, while such influence needs a further study to

investigate vehicle behaviors at merge segment. As for

geometric variation, on ramps in NEX are virtually allo-

cated far from poor alignment like small curve. Thus, it is

considered reliable that the significance of geometric var-

iation affecting crashes is lower at merger segment com-

pared to basic segment.

At diverge segment, the most significant difference from

basic and merge segments is that the DR and the vertical

variation h are related to the 1st component. Higher DR can

significantly interrupt mainline traffic since it is necessary

to pass through several lanes to move onto the deceleration

lane for driving vehicles. Furthermore, higher h can make

lane-changing maneuvers more difficult.

Generally, sharp curve has much worse design consis-

tency compared to other segments. Crashes at sharp curve

are found to be associated with poor vertical consistency

(ISD and h), high horizontal variation ICF along with speed

v, low traffic density k in nighttime, wet pavement, and

holiday. In NEX, sharp curve is often designed to connect

routes with different elevations. Thus, the vertical consis-

tency is fairly poor. Smaller radius along with high v may

cause notable centrifugal force. The affecting mechanisms

of other component are similar to these at basic, merge, and

diverge segments.

5.2.2 High-density uncongested flow

As traffic density increases, the inter-vehicle interaction

gets more intensive. The corresponding results of PCA in

high-density uncongested flow are summarized in

Table 11. All of the components are of statistical

significance.

In the case of high-density uncongested flow, it is dis-

tinct that traffic-related variables including k and v become

an independent component, as a reflection of the increased

interaction of vehicles. Furthermore, in terms of the value

of loading, high density not low density is adverse to

safety. The finding can further support the results of CR

models: CR is decreasing to k in low-density uncongested

flow, while it is increasing in high-density uncongested

flow.

With respect to the differences by facility type, at merge

segment, MR gets to be a factor related to the 1st com-

ponent due to the increased interruption of ramp traffic

with the increase of traffic density. During the variation in

traffic conditions, the significance of DR becomes lower

than geometric variation at diverge segment. However, in

high-density uncongested flow, LD is more important in

contrast to low-density uncongested flow. Once a driver

feels the difficulty for lane-changing maneuvers in

diverging area, they may move onto the nearest lane to off-

ramp in advance in the upstream of diverging area. As a

result, the impact of lane-changing maneuvers on mainline

traffic gets relatively low. In a sharp curve, crashes are still

found to be probable with a decrease in k, which is similar

to the tendency of CR model.

5.2.3 Congested flow

With the further increase of traffic density, congested flow

appears. In the same way, Table 12 summarizes the results

of PCA by facility type in congested flow.

Table 10 PCA results in low-density uncongested flow

Facility type (number of crash) Item Principal component

1st 2nd 3rd 4th 5th

F L F L F L F L F L

Basic segment (225) Component ICF 0.953 k -0.852 v 0.798 h 0.973

ISD 0.959 Light 0.838 Pave 0.783


Merge segment (140) Component ICF 0.867 k -0.841 MR 0.808 v 0.721 Day 0.874

ISD 0.901 Light 0.869 LA 0.747 Pave 0.742

Percent of variance 20.1 18.8 15.4 13.9 11.9

Diverge segment (167) Component DR 0.807 ICF 0.948 k -0.807 v 0.892 LD 0.797

h 0.845 ISD 0.746 Light 0.860 Pave 0.848


Sharp curve (319) Component ISD 0.854 ICF 0.948 k -0.820 Pave 0.929 Day 0.981

h 0.978 v 0.753 Light 0.794


F factor, L loading

232 Y. Wu et al.

123 J. Mod. Transport. (2013) 21(4):224–235

Table 12 demonstrates that the effect of traffic flow on

crashes get more important in congested flow, compared to

that in uncongested flow. Except merge segment, the sig-

nificance of traffic flow affecting crashes is the highest.

Based on the percent of variance, the influence of geo-

metric design is further decreasing.

Regarding the differences by facility type, crashes at

merge segment are found to be positively associated with

smaller LA, not higher LA. For congested flow, smaller LA

may increase the difficulty of adequate speed adjustment

for merging and lane-changing maneuvers. Besides, based

on the loading of day type, weekday not holiday is a sig-

nificant factor. It is likely related to higher percentage of

heavy vehicles on weekday that may induce more frequent

shockwave in congested flow. At diverge segment, as

similar to merge segment, weekday is also a significant

factor. Meanwhile, smaller LD not higher LD is adverse to

safety. At sharp curve, poor ambient light can significantly

restrict visibility, while visibility is critical for driving in

small inter-vehicle spacing. Thus, ambient light becomes

another important factor in congested flow compared to

high-density uncongested flow.

From the analyses above, geometric features are found

out to be the most significant influencing factor in uncon-

gested flow. In this sense, the different CR characteristics

by facility type in uncongested flow may be significantly

associated with the variation in geometry. Poor design

consistency induced by small radius is the potential cause

for the highest CR in sharp curve. Ramp traffic can inter-

rupt mainline traffic, and longer acceleration lane may

provide longer interruption area. Both features can increase

crash risk at merge segment. A lot of diverging traffic may

move onto the lane nearest to deceleration lane in advance

in the upstream of diverging area, since urban expressway

carries a lot of commuters and many drivers are familiar

with road structure. Hence, even if DR and LD are found

out as significant influencing factors, CR at diverge seg-

ment is not significantly higher than that at basic segment.

As traffic density increases, the effects of traffic-related

variables increase and get more significant than geometry

in congested flow. In this condition, once a breakdown

initiates at bottlenecks, it can propagate to upstream section

that may consists of several facility types, where traffic

conditions are not significantly different. As a result, the

difference of CR characteristics at basic, merge, and

diverge segments is not significant. However, due to the

heavily restricted visibility induced by the special geo-

metric design, sharp curve still has higher CR than other

facility types.

6 Conclusions and future work

This paper identified the different CR characteristics by

facility type of Nagoya Urban Expressway. In uncongested

flow, CR at basic, merge, and diverge segments appears

convex downward to traffic density. In contrast, the value

at sharp curve follows a decreasing tendency. In congested

flow, CR at four facility types increases as traffic density

increases. In both un- and congested flows, sharp curve has

the worst safety performance in view of its highest CR

among the four facility types. As for other segments, merge

Table 11 PCA results in high-density uncongested flow


1st 2nd 3rd 4th 5th

F L F L F L F L F L

Basic segment (94) Component ICF 0.983 k 0.858 Day 0.776 h 0.925

ISD 0.974 v -0.885 Light 0.781


Merge segment (112) Component MR 0.818 k 0.936 LA 0.842 Day 0.810 Pave 0.963

ICF 0.923 v -0.899 Light 0.713

ISD 0.960


Diverge segment (37) Component ICF 0.970 DR 0.904 k 0.793 h 0.733 Pave 0.913

ISD 0.977 LD 0.772 v -0.704


Sharp curve (122) Component ICF 0.723 k -0.901 Pave 0.901 Day 0.869

ISD 0.962 v 0.872

h 0.908



123J. Mod. Transport. (2013) 21(4):224–235

segment has higher CR compared to the basic and diverge

segments in uncongested flow. Comparatively, CR at three

facility types is not significantly different in congested

flow.

The causes of the differences were further investigated

by focusing on traffic conditions and considering the

interaction of geometry, traffic flow, and ambient condi-

tions. Generally, geometric features are the most significant

factors in uncongested flow. With the increase of traffic

density, the effects of traffic-related variables increase and

become most significant in congested flow. For ramp

traffic, the significance of MR affecting crashes is on the

rise as mainline flow increases. In contrast, the significance

of DR gets decreasing. In addition, higher LA and LD are

adverse to safety for uncongested flow, while smaller LA

and LD are adverse for congested flow. Crashes at sharp

curve are highly associated with the after effects of its

special geometric design, such as large centrifugal force

and heavy restricted visibility.

The potential benefits of integrating these findings in

safer geometric design and traffic control are numerous.

The analysis can provide a basis for geometric audit for

safety regarding design consistency. Meanwhile, based on

the estimated CR models, road administrators can easily

image the safety performance with the variation of traffic

conditions at a given facility type. Furthermore, PCA

results may help prioritize countermeasures and further

estimate the safety performance of an adopted

countermeasure.

For more accurate analysis of crash characteristics, data

in smaller time window, e.g., 1 min even 30 s, are highly

recommended to improve the reliability of statistics, since

crash occurrence is significantly associated with the short-

term turbulence of traffic flow [1]. Furthermore, it is better

to examine the effect of inter-lane interaction on crashes if

the lane-based data is available. In this study, ramp traffic

is found out to play a significant role for safety at merge

and diverge segments. Thus, a microscopic analysis on

driver behavior is needed. In essence, PCA is a qualitative

analysis and the results are insufficient for applying spe-

cific countermeasures for a given case. Future studies are

expected to acquire the quantitative effects of various

influencing factors on crashes.

Acknowledgments The authors gratefully acknowledge the support

of Nagoya Expressway Public Corporation for the data provision and

other helps for this study.

Open Access This article is distributed under the terms of the

Creative Commons Attribution License which permits any use, dis-

tribution, and reproduction in any medium, provided the original

author(s) and the source are credited.

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Table 12 PCA results in congested flow


1st 2nd 3rd 4th 5th

F L F L F L F L F L

Basic segment (138) Component k 0.950 ICF 0.842 h 0.699 Day 0.942

v -0.947 ISD 0.743 Pave 0.814


Merge segment (91) Component MR 0.871 k 0.883 ICF 0.672 LA -0.871 Day -0.933

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Sharp curve (27) Component k -0.772 ICF 0.909 Pave 0.799 Day 0.912

v 0.950 ISD 0.875 0.949

h 0.971 Light


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